Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations. (English) Zbl 1203.65255
Summary: We numerically verify that the non-symmetric interior penalty Galerkin method and the Oden-Babusǩa-Baumann method have sub-optimal convergence properties when measured in the \(L ^{2}\)-norm for odd polynomial approximations. We provide numerical examples that use piece-wise linear and cubic polynomials to approximate a second-order elliptic problem in one and two dimensions.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
References:
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